Sentence examples for defining the solution from inspiring English sources

Defining the solution representation of the system is the first task of applying GA.

Proof First, we introduce the function v ( n ) = x ( 0 ) ( 1 − λ 1 / α ) n, n ∈ Z. defining the solution of the Volterra convolution equation with infinite delay v ( n + 1 ) = ∑ j = − ∞ n a ( n − j ) v ( j ), n = 0, 1, …, (4.7).

The integral curves of the section ˘ ξ h Open image in new window (Equation 110) (with induced vector field ρ * π ( ξ ˘ h ) ) Open image in new window, defining the solution of Equation 111, satisfy the Hamilton equations for h ˘ ( x i, p a ) Open image in new window, d x i dt = ρ a i ∂ h ˘ ∂ p a, d p a dt = - C ab e p e ∂ h ˘ ∂ p b + ρ a i ˘ h ∂ ∂ x i. Open image in new window (112).

However, as metabolite flux minimisation only alters the objective function and not the constraints defining the solution space, it is amenable to the same strategy that is used for speeding up FVA [ 53] and, thus, is more computationally efficient.

Now, we know that in cryptic puzzles either the beginning or the end of the clue defines the solution; the rest provides a different way to get the same sequence of letters.

Von Neumann and Morgenstern defined the solution to an n-person game as a set of imputations satisfying two conditions: (1) no imputation in the solution dominates another imputation in the solution and (2) any imputation not in the solution is dominated by another one in the solution.

A standard approach in deriving the mild solution of (1.1) is define the solution operator Q.

In order to define the solution for the problem (1.1 - 1.2 1.1 - 1.2 the followeneedemma.

In order to define the solution for the problem (1.1), we need the following lemmas.

In order to define the solution of problem (1.6), we shall consider the following space.

This lemma is used to define the solution of the boundary value problem (1.5)–(1.5).